Regularization methods in Banach spaces

Inverse and ill-posed problems depend on regularization, a set of techniques that yield stable approximate solutions. Their mathematical models usually take the form of first-kind operator equations, and the forward operator is often defined between Hilbert spaces. The authors argue that this choice frequently reflects convention more than a realistic model, and that Banach spaces often describe the situation more faithfully. Sparsity constraints built on general Lp norms and the BV norm have also become widely used.

The best-known regularization methods have been studied for linear and nonlinear operator equations in Banach spaces. This monograph gathers those results into a single volume.